Cache available post types on each sub site in admin

[AaronHolbrook]

Having to query each site every time causes a noticeably slow user experience on the admin page. Would be good to cache this in settings and inject/remove post types once the query has been performed (possibly also cache this for a small period of time and invalidate on permalink/rewrite flush).

[tlovett1]

This could be useful to cache if you made sure your invalidation strategy was flawless. Having someone choose a post type that is not available could be dangerous. I don't imagine people will really be touching the settings page very often so I think this is pretty minor.

[tlovett1]

Punting. This is useful but not required for V1.